Calculus Examples

$lim_{x \to 2} \arctan (\frac{x^{2} - 4}{3 x^{2} - 6 x})$

Step 1

Simplify the denominator.

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Step 1.1

Multiply $3$ by $2$ .

$\frac{2}{6 - 1 \cdot 3}$

Step 1.2

Multiply $- 1$ by $3$ .

$\frac{2}{6 - 3}$

Step 1.3

Subtract $3$ from $6$ .

$\frac{2}{3}$

Step 2

Substitute $t$ for $\frac{x^{2} - 4}{3 x^{2} - 6 x}$ and let $t$ approach $\frac{2}{3}$ since $lim_{x \to 2} \frac{x^{2} - 4}{3 x^{2} - 6 x} = \frac{2}{3}$ .

$lim_{t \to \frac{2}{3}} \arctan (t)$

Step 3

Evaluate the limits by plugging in $\frac{2}{3}$ for all occurrences of $t$ .

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Step 3.1

Simplify the denominator.

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Step 3.1.1

Multiply $3$ by $2$ .

$\arctan (\frac{2}{6 - 1 \cdot 3})$

Step 3.1.2

Multiply $- 1$ by $3$ .

$\arctan (\frac{2}{6 - 3})$

Step 3.1.3

Subtract $3$ from $6$ .

$\arctan (\frac{2}{3})$

Step 3.2

Evaluate $\arctan (\frac{2}{3})$ .

$0.5880026$